Example:
Peter got a perfect/flawless/impeccable score: 0 errors for 100 questions.
John got a ? score: 100 errors for 100 questions (Yes, he filled out the questions. And probably smudged with the extra benefit of grammatical and spelling errors in hen scratching).
The problem with "normal" antonyms is that they fit a range of results. The words "worst possible" or "best possible" are sounding more than statements than judgements. "Perfect"/"Impeccable" contains the information that it not only contains no errors, it gives the impression that it should not contain errors.
The searched word should immediately inform the reader that if something is measured on a scale, this result is the worst possible result. Beyond fubar. We hit the rock bottom. A perfect screw-up.
EDIT: If there is no such word and I am stuck with "worst possible", that would be nice to know, too. But I must admit, the "unworsenable score" has something...